Determining a one-tailed upper limit for future sample relative reproducibility standard deviations

A formula was developed to determine a one-tailed 100p% upper limit for future sample percent relative reproducibility standard deviations (RSD(R),%= 100s(R)/y), where S(R) is the sample reproducibility standard deviation, which is the square root of a linear combination of the sample repeatability variance (s(r)2) plus the sample laboratory-to-laboratory variance (s(L)2), i.e., S(R) = s(L)2, and y is the sample mean. The future RSD(R),% is expected to arise from a population of potential RSD(R),% values whose true mean is zeta(R),% = 100sigmaR, where sigmaR and mu are the population reproducibility standard deviation and mean, respectively.